A Review of GRACE/GRACE-FO Satellite Gravimetry Applications in Earthquake Activity Monitoring

Abstract

Earthquakes induce significant mass redistribution, generating temporal gravity variations detectable by GRACE and GRACE-FO missions. However, the capability of different gravity field recovery strategies, particularly spherical harmonic (SH) and mass concentration (MASCON) solutions, to capture coseismic signals remains insufficiently quantified. This study investigates coseismic gravity changes associated with three Mw 9.0-class earthquakes, including the 2004 Sumatra–Andaman, 2010 Maule, and 2011 Tohoku events, using both SH and MASCON products and theoretical dislocation models. Spectral analysis indicates that recovered signals are dominated by long-wavelength components, while short-wavelength deformation is strongly attenuated. SH products exhibit higher sensitivity to large-scale mass redistribution but are more affected by striping noise and leakage, whereas MASCON products provide improved stability at the cost of signal attenuation. Overall, these findings highlight fundamental limitations of current GRACE-derived products in fully recovering coseismic deformation signals and emphasize the need for improved signal separation strategies.

1. Introduction

Earthquakes are among the most destructive natural hazards, posing severe threats to human life and property. Monitoring seismic activity is therefore essential for improving earthquake prediction, assessing the extent of post-event damage, and characterizing crustal deformation following major events.

A variety of geodetic techniques have been developed for earthquake monitoring. Early studies relied on ground-based gravity measurements, which revealed that temporal variations in the gravity field are closely associated with earthquake preparation, occurrence, and postseismic adjustment processes. Field observations from several major earthquakes, including the Xingtai, Jiuzhaigou, and Wenchuan events, have further demonstrated the feasibility and effectiveness of mobile gravity monitoring in seismic studies [1,2,3]. These observations highlight the potential of gravity data for detecting large-scale mass redistribution related to seismic events.

Gravity observations provide valuable constraints on mass redistribution associated with seismic events. However, they cannot fully resolve the spatial and temporal characteristics of seismic surface deformation. GNSS/GPS observations also play a fundamental role in earthquake geodesy by providing high-precision, continuous three-dimensional ground displacement measurements, serving as an important complement to InSAR in constraining surface deformation. With the advancement of spaceborne observation technologies, Interferometric Synthetic Aperture Radar (InSAR) has become a widely used tool for measuring surface deformation [4]. By exploiting interferometric phase differences, InSAR enables millimeter-level monitoring of ground displacement over large areas and has been extensively applied to the inversion of earthquake source parameters and slip distributions, providing critical constraints on fault geometry and rupture processes [5,6,7,8,9,10]. However, InSAR primarily captures surface deformation and is less sensitive to subsurface mass redistribution processes, particularly at large spatial scales.

These limitations underscore the need for complementary approaches that can directly observe mass changes within the Earth system, a capability afforded by satellite gravimetry through measuring spatiotemporal variations in the Earth’s gravity field to provide unique constraints on mass redistribution associated with major earthquakes. Satellite gravimetry—particularly data from GRACE and GRACE-FO—has enabled systematic observation of global gravity field variations linked to geophysical processes; in contrast to ground-based gravity measurements, these missions deliver global coverage, consistent long-term observations and improved sensitivity to large-scale mass changes. GRACE operated from 2002 to 2017, succeeded by GRACE-FO in 2018, and these datasets have been widely utilized to investigate coseismic and postseismic gravity changes associated with major earthquakes. Compared with existing reviews, this study provides a more systematic synthesis of recent advances in earthquake research using GRACE/GRACE-FO data. This review highlights three key contributions: first, it provides a critical comparison of different gravity field products (spherical harmonic and mascon solutions) and discusses how variations in data processing affect the characterization of coseismic signals; second, it assesses hydrological and other environmental mass variations as primary noise sources, and summarizes recent signal separation and noise reduction methods, including filtering and decorrelation techniques; third, it emphasizes the complementarity between GRACE-derived gravity changes and InSAR observations, clarifying their respective sensitivities to volumetric mass redistribution and surface deformation. By integrating these perspectives, this review establishes a unified framework for interpreting satellite gravimetry signals in earthquake studies, and identifies key limitations that remain obstacles to robust earthquake source characterization.

This review is based on a systematic search of scientific literature using major academic databases, including Web of Science and Scopus, with searches conducted using combinations of keywords such as “satellite gravimetry”, “GRACE”, “GRACE-FO”, “earthquake”, “coseismic deformation”, and “postseismic mass redistribution. The selected studies primarily cover the period from 2002 to 2025, corresponding to the operational timeline of the GRACE and GRACE-FO missions, and only peer-reviewed journal articles focusing on the application of satellite gravimetry to earthquake-related processes were included. Studies were further screened based on relevance, methodological rigor, and availability of quantitative analysis, with articles not directly related to seismic mass redistribution or lacking sufficient methodological detail excluded.

The remainder of this paper is organized as follows: Section 2 introduces GRACE/GRACE-FO measurement principles and mission characteristics; Section 3 overviews gravity field solutions and their uncertainties; Section 4 reviews their earthquake applications, including SH/mascon approaches and comparisons; Section 5 discusses key challenges and future directions; and Section 6 summarizes main conclusions.

2. Overview and Comparison of GRACE and GRACE-FO Missions

The Gravity Recovery and Climate Experiment (GRACE) mission was jointly developed by the National Aeronautics and Space Administration (NASA) and the German Aerospace Center (DLR) and was launched in late 2001. The mission employed a low–low satellite-to-satellite tracking (SST) configuration consisting of two low-Earth-orbit satellites flying along the same orbit with an along-track separation of approximately 200 km. In addition to onboard GPS receivers used for precise orbit determination, the inter-satellite distance and its rate of change were continuously measured with micrometer-level accuracy. Temporal variations in the Earth’s gravity field were derived from these inter-satellite range measurements. The nominal orbital altitude of the GRACE satellites was approximately 500 km [11]. GRACE and GRACE-FO quantify temporal variations in the Earth’s gravity field through precise monitoring of the range between two co-orbiting satellites. As the satellite pair traverses regions with anomalous mass distribution, spatial gravity field variations induce differential accelerations between the leading and trailing satellites, thereby inducing minor fluctuations in their inter-satellite separation distance. Measured with high precision via microwave ranging (GRACE) or laser interferometry (GRACE-FO), these inter-satellite range variations constitute the primary observables of the mission. Integration of these range measurements with precise orbit determination and dynamic modeling enables inversion of the observed range variations to retrieve time-variable gravity field coefficients, which can then be interpreted to elucidate mass redistribution processes occurring on and within the Earth.

The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) [12,13,14] mission was launched on 22 May 2018 to continue the scientific observations of the original GRACE mission conducted between 2002 and 2017. GRACE-FO introduced a laser ranging interferometer operating in parallel with the microwave ranging system which significantly improved the precision of inter-satellite range change measurements to the sub-micrometer level. The laser system shows enhanced performance in monitoring low-frequency signals such as ice mass variations. However, despite the intended continuity between the two missions, an approximately 11-month data gap persists between June 2017 and May 2018, resulting from the transition from GRACE to GRACE-FO. This temporal discontinuity presents challenges for the analysis of continuous time series, particularly for postseismic processes that evolve over timescales comparable to or shorter than the gap duration. Consequently, the interpretation of gravity changes associated with earthquakes occurring near the end of the GRACE mission or during the gap period may be compromised, often requiring the adoption of interpolation strategies or complementary geodetic observations [15,16,17].

A comparison of the main parameters of GRACE and GRACE-FO is provided in

Table 1. Comparison between the GRACE and GRACE-FO missions.

Parameter	GRACE	GRACE-FO
Launch date	March 2002	May 2018
Mission duration	15 years	At least 10 years (expected to operate until ~2030)
Satellite configuration	Twin satellites	Twin satellites
Ranging instrument	Microwave ranging system	Microwave ranging system; Laser Ranging Interferometer (LRI)
Orbital altitude	~500 km	~490 km
Spatial resolution	~300–400 km	~300–400 km
Temporal resolution	Monthly	Monthly
Data characteristics	First mission to provide time-variable global gravity field observations	Continuation of GRACE observations with improved ranging precision enabled by LRI

.

3. Principles of Satellite Gravimetry for Earthquake Monitoring

3.1. Observation Principle of GRACE and GRACE-FO

During fault rupture, coseismic deformation occurs as crustal blocks slip along the fault plane, resulting in spatial displacement of rock masses. This process leads to surface subsidence or uplift and is accompanied by changes in surface elevation and mass distribution. The redistribution of mass within the crust and at the Earth’s surface induces perturbations in the local gravity field. Consequently, variations in surface gravity anomalies ($\Delta g$) are directly related to changes in mass ($\Delta M$), providing a physical basis for detecting earthquake-related processes using satellite gravimetry.

$$\Delta g={\displaystyle \frac{G}{r^2}}\cdot \Delta M$$

(1)

In Equation (1), $G$ denotes the gravitational constant, $r$ represents the satellite orbital radius, which is approximately 500 km, and $\Delta M$ refers to surface or subsurface mass variations expressed in kilograms.

Following a major earthquake, the crust and upper mantle continue to deform over extended timescales. Viscoelastic relaxation at the lithosphere–asthenosphere boundary leads to a gradual evolution of mass distribution, which manifests as long-term postseismic gravity changes detectable by GRACE and GRACE-FO observations.

Temporal variations in the Earth’s gravity field induce perturbations in satellite altitude and velocity. The GRACE/GRACE-FO twin satellites continuously measure minute changes in their inter-satellite distance using precise ranging systems, from which subsurface mass variations can be inferred. In practice, GRACE-derived gravity field variations are commonly expressed in terms of equivalent water height (EWH) [15], which represents gravity potential changes in a mass-equivalent form and is typically reported in millimeters or centimeters.

The relationship between equivalent water height and mass change is given by (2)

$$EWH={\displaystyle \frac{\Delta \sigma }{\rho }}$$

(2)

In Equation (2), $\rho$ denotes the density of water, and $\Delta \sigma$ represents the mass change per unit area (kg/m²).

The relationship between gravity anomalies and mass change can also be expressed as (3)

$$\Delta \sigma ={\displaystyle \frac{\Delta V}{4\pi GR}}$$

(3)

In Equation (3), $R$ is the mean radius of the Earth, and $\Delta V$ denotes the gravity potential anomaly (m²/s²).

However, the reliability of GRACE-derived gravity field solutions is inherently scale-dependent, necessitating the evaluation of their accuracy and uncertainty characteristics. The accuracy of GRACE and GRACE-FO gravity field models is commonly evaluated using both spectral error characteristics and equivalent water height (EWH) uncertainties, which provide complementary descriptions in the spectral and spatial domains, respectively. At effective spatial resolutions of approximately 300–400 km, the uncertainty of monthly gravity solutions is generally on the order of 1–2 cm in terms of EWH. However, at smaller spatial scales, the uncertainty increases significantly due to the amplification of high-degree noise in the spherical harmonic coefficients, which limits the reliable recovery of short-wavelength mass variations [18].

In the spectral domain, gravity field solutions are represented by spherical harmonic coefficients. Their errors generally increase with harmonic degree due to measurement noise and inversion instability, reducing reliability at high spatial frequencies. These correlated errors typically appear as characteristic north–south striping patterns in raw gravity solutions. Decorrelation filtering and spatial smoothing methods, including Gaussian and DDK filtering, are commonly adopted in post-processing to mitigate such artifacts [19,20].

The accuracy of GRACE and GRACE-FO gravity models is usually evaluated by spectral error characteristics and equivalent water height (EWH) uncertainties, which provide complementary descriptions in the spectral and spatial domains. At effective spatial resolutions of approximately 300–400 km (the typical smoothing scale for GRACE data), monthly gravity solutions show EWH uncertainties on the order of 1–2 cm. Nevertheless, high-degree noise amplification at smaller spatial scales limits the reliable recovery of short-wavelength mass variations.

These limitations indicate that GRACE-derived gravity fields are better suited for large-scale mass redistribution signals, whereas smaller-scale or high-frequency processes—such as localized coseismic deformation—may be underestimated or spatially smoothed.

3.2. Dislocation Models and Their Characteristics

To link the gravity changes observed by GRACE/GRACE-FO with specific earthquake processes, it is necessary to employ seismic dislocation theory models to describe crustal deformation induced by source rupture and the associated redistribution of mass. Okubo systematically derived analytical expressions for gravitational potential and gravity changes induced by shear and tensile fault dislocations within an elastic half-space framework. The study clearly demonstrated that fault slip affects the gravity field through the combined contributions of surface deformation, volumetric strain within the medium, and the free-air effect. This theoretical formulation established a fundamental basis for the quantitative modeling of coseismic and postseismic gravity changes associated with earthquake faulting processes.

3.2.1. Rectangular Fault Model in an Elastic Half-Space

Okada [5,6] derived closed-form analytical solutions in 1985 for slip on a finite rectangular fault embedded in an isotropic, elastic half-space. These solutions allow the calculation of surface displacements, strain fields, and gravity changes in three dimensions. The model is based on linear elastic constitutive relations and assumes a homogeneous, isotropic, and infinitely extending half-space. Under these assumptions, the governing equations can be solved analytically using Green’s function methods [21,22]. The fault plane is represented as a rectangular surface defined by five parameters, including fault length (L), width (W), lower-edge depth (d), strike angle, and dip angle.

3.2.2. Spherically Symmetric Earth Model

Sun et al. developed analytical dislocation solutions based on a spherically symmetric, linear elastic Earth model, enabling direct computation of gravity potential and gravitational acceleration changes at arbitrary locations [23]. Compared with the rectangular fault model in a half-space, the spherical formulation accounts for Earth curvature and the global elastic structure, making it more suitable for simulating long-wavelength gravity field variations. This model is therefore well matched to low-degree spherical harmonic gravity signals and is particularly applicable to GRACE-based monthly gravity field analyses.

3.2.3. Spherical Dislocation Theory

Spherical dislocation theory was initially proposed in the 1990s based on spherically symmetric Earth models and was later extended to explicitly describe gravity changes induced by fault slip. Pollitz et al. [24] further refined the computation of Love numbers [25] within a spherical Earth framework, providing a theoretical foundation for mapping fault slip onto gravity field variations. Using Green’s functions or Love numbers, this approach establishes a direct link between seismic sources, surface deformation, and gravity changes, allowing gravity perturbations to be predicted at any observation point within a spherically symmetric Earth model.

The Love number kn^(ij) is used to describe the gravitational potential response of the n-th spherical harmonic component under compressional loading (Equation (4)).

$$\Delta V(\theta ,\varphi )={\displaystyle \sum _{n=0}^{\infty }{\displaystyle \sum _{m=-n}^n{k}_n^{(ij)}}}{U}_{ij}{Y}_n^m(\theta ,\varphi )$$

(4)

In Equation (4), $U_{ij}$ denotes the dislocation component, $Y_n^m$ represents the spherical harmonic function, $n$ and $m$ are the degree and order, respectively, $\theta$ ∈ [0, π] denotes polar angle, and $\varphi$ ∈ [0, 2π) denotes azimuth angle.

Spherical dislocation theory has been widely applied in the analysis of coseismic gravity changes and postseismic recovery processes. The spherically symmetric Earth model, which assumes a layered and radially stratified structure, accounts for Earth curvature and radial heterogeneity and is therefore well suited for modeling long-wavelength gravity signals associated with low-degree spherical harmonics, consistent with the observation scale of GRACE. However, its ability to resolve near-field, small-scale deformation is limited compared with that of half-space models. In contrast, the rectangular fault elastic half-space model assumes a homogeneous, isotropic elastic medium and provides closed-form solutions for surface displacements induced by finite rectangular fault slip, offering high computational efficiency and compact analytical expressions.

Overall, dislocation theory provides the essential physical framework for quantitatively linking earthquake fault slip processes with the long-wavelength gravity variations observed by GRACE and GRACE-FO, and thus constitutes an indispensable theoretical foundation for satellite gravimetry-based earthquake monitoring.

4. Applications of GRACE/GRACE-FO Gravity Products in Earthquake Studies

This section reviews the applications of GRACE and GRACE-FO gravity field products in earthquake-related studies, with an emphasis on their capability to detect and interpret coseismic gravity changes, as well as to monitor postseismic deep mass redistribution; it also focuses on hydrological noise and the advancement of signal separation techniques, along with the comparison between different gravity field solutions. Specifically, two mainstream methods are widely employed for gravity field recovery in these studies: mass concentration (MASCON) solutions and spherical harmonic (SH) products [26,27]. MASCON solutions, characterized by superior spatial localization and reduced signal leakage, excel in regional-scale studies, while SH products, which represent the global gravity field via spectral expansion, offer flexibility in global-scale analysis but are more susceptible to noise and signal attenuation.

To ensure clarity, this section is organized based on the methodological characteristics of these two solutions—Section 4.1 focuses on MASCON solutions and their advantages in signal recovery, Section 4.2 addresses SH products, their application potential, and the associated challenges of noise and signal leakage, and Section 4.3 presents a comparative analysis of the two methods to clarify their respective strengths, limitations, and applicability in earthquake-related research, thereby providing a comprehensive overview of the application progress, remaining challenges, and methodological advancements of satellite gravimetry in earthquake studies.

4.1. Applications of MASCON Products

In the context of earthquake research, GRACE observations of coseismic and postseismic mass redistribution indicate that large earthquakes can generate detectable signals in the broad-scale gravity field, providing a physical basis for describing earthquake-induced mass migration using mascon solutions. Subsequent studies further showed that the enhanced regional localization capability of mascon solutions facilitates the extraction of gravity signals associated with earthquake processes from complex background variations, thereby offering new observational constraints on source rupture characteristics and postseismic deformation. Following the launch of GRACE-FO, the RL06 mascon product released by JPL has been systematically validated in terms of algorithmic stability and long-term consistency, establishing mascon solutions as a key data foundation for analyzing a wide range of solid Earth mass change processes, including earthquakes [28]. Building on these advantages, MASCON products—with their enhanced spatial localization and mitigated signal leakage—have been extensively employed in diverse geophysical investigations including those of terrestrial water storage, glacier and ice sheet mass balance, ocean bottom pressure variations, and earthquake-related mass redistribution [29,30,31,32], and they exhibit considerable potential for detecting large-scale mass redistribution associated with major earthquakes.

Early studies have demonstrated that direct estimation of equivalent mass variations in the spatial domain allows the characterization of regional-scale mass migration processes with enhanced spatial resolution [33]. Relative to conventional spherical harmonic solutions, mascon-based approaches present distinct advantages in suppressing striping noise and mitigating signal leakage, as validated by their successful applications in investigations of ice sheet mass balance and sea-level change [34]. To further enhance signal fidelity, various post-processing strategies have been developed to alleviate leakage effects. For instance, a coastline-resolution-enhanced filtering method separates land and ocean mass signals in mascons intersecting coastal boundaries via weighted least squares with prior constraints from GLDAS and ECCO2, and global gain factors have been introduced to compensate for short-wavelength signal attenuation induced by mascon parameterization. Combinations of these methods have been verified to effectively reduce leakage-related errors [35]. Similarly, signal separation techniques have been integrated into mascon data processing. As an example, principal component analysis has been utilized to build multi-earthquake models and suppress non-seismic disturbances, thereby facilitating more robust extraction of earthquake-related gravity signals [36].

Save H et al. [35] developed a high-resolution CSR RL05 mascon solution from GRACE observations, parameterizing the gravity field on a 1° equal-area geodesic grid and regularizing it via a time-variable Tikhonov scheme without reliance on external model constraints. This approach effectively mitigates the north–south striping errors pervasive in unconstrained spherical harmonic solutions [37]. Quantitative comparison between theoretical gravity changes from dislocation models and filtered MASCON solutions shows that GRACE-based mascon products recover only a small fraction of the original coseismic signal. For the three Mw 9.0 earthquakes analyzed here, amplitude ratios of mascon-derived signals to unfiltered theoretical values are ~0.51% (2011 Tohoku), 5% (2004 Sumatra), and 7% (2010 Chile), with an overall average of ~1%—the Tohoku earthquake exhibiting the most pronounced attenuation. This significant attenuation stems from intrinsic limitations of mascon-based gravity field recovery. Spectral decomposition further shows that recovered signals are concentrated primarily in low-degree components (≤60 spherical harmonic degree), accounting for nearly 50% of retained energy, while higher-degree components (>60)—more closely linked to fine-scale coseismic deformation—contribute only ~7% and are largely suppressed or contaminated by gridding and reconstruction artifacts. These findings collectively show that mascon solutions naturally prioritize long-wavelength mass redistribution signals while strongly attenuating short-wavelength coseismic deformation, limiting their ability to fully reconstruct the true theoretical gravity signal from earthquake processes [38].

Overall, existing studies demonstrate that mascon-based GRACE/GRACE-FO solutions offer a robust framework for detecting and interpreting earthquake-induced mass redistribution from regional to global scales. Their superior spatial localization, along with reduced striping noise and signal leakage, facilitates effective separation of seismic gravity signals from complex background variations. Meanwhile, methodological advances in filtering, signal separation and parameterization have further enhanced the reliability and interpretability of mascon products [39]. Nevertheless, these solutions inherently emphasize long-wavelength gravity signals, leading to significant attenuation of short-wavelength coseismic signals. Consequently, although mascon approaches perform well in capturing large-scale mass migration and postseismic processes, they still face limitations in fully recovering fine-scale coseismic gravity signals and reconstructing complete theoretical signals.

4.2. Applications of Spherical Harmonic (SH) Products

Spherical harmonic (SH) products represent temporal variations in the global gravity field through spherical harmonic expansion coefficients and constitute one of the two primary data representations provided by the GRACE and GRACE-FO missions. Compared with regionally constrained MASCON solutions, SH products are better suited for investigating large-scale and long-term mass redistribution processes and long-wavelength rheological responses at depth. The temporal resolution is typically monthly, while the effective spatial resolution is controlled by the truncation degree and applied filtering and smoothing strategies. SH products have been applied to investigate coseismic and early postseismic gravity signals associated with several great earthquakes and to track long-term postseismic viscoelastic relaxation and deep mass migration. Their application is limited by hydrological noise and spatial leakage, making additional filtering and correction procedures necessary.

4.2.1. Detection of Coseismic Gravity Changes

Since the launch of GRACE, spherical harmonic (SH) products have been applied to detect coseismic gravity signals and have demonstrated that earthquakes producing deformation with sufficiently large spatial extent and amplitude can generate detectable gravity anomalies in monthly SH solutions. Such signals are typically associated with great earthquakes, with moment magnitudes on the order of Mw ≥ 8. Studies of major events, including the 2004 Sumatra–Andaman earthquake the 2010 Maule earthquake in Chile and the 2011 Tohoku earthquake in Japan, indicate that SH-observable coseismic gravity changes arise from both mass redistribution related to fault slip and perturbations of near-surface density interfaces induced by vertical surface displacements. In contrast, earthquakes of smaller magnitude, generally below Mw ≈ 7.5, remain difficult to resolve using SH products.

To systematically synthesize the methodological development of SH (Spherical Harmonics)-based coseismic gravity studies, representative earthquake cases spanning shallow megathrust and deep-focus events are compared in a unified framework where these studies adopt distinct signal extraction strategies—direct differencing, filtering-enhanced techniques, and gradient-based methods—to tackle the core challenge of extracting weak gravity perturbations buried in noisy satellite observations, a task critical for unraveling coseismic gravity field evolution and constraining Earth’s interior structural responses to seismic events. Shallow megathrust events demand high-precision perturbation recovery while deep-focus studies require robust noise suppression to capture subtle gravity changes, and

Table 2. Summary of SH-based coseismic gravity studies across different earthquake types.

Earthquake	Key Technique	Main Findings	Advancement	Limitations	Study
Sumatra–Andaman earthquake	Pre–post GRACE differencing	First detection of crustal dilatation	First detection of coseismic signal	Limited to large events	Han et al. [40]
	Wavelet analysis	Coseismic + postseismic separation	Multi-scale signal extraction	Model dependence	Panet et al. [41]
	Gaussian + Fan filter + GPS	Large-scale gravity anomalies	Improved spatial resolution	Signal attenuation	Wang et al. [42]
	Gravity gradient tensor	Clear fault-related patterns	Enhanced spatial localization	Noise amplification	Wang et al. [43]
Tohoku-Oki earthquake	Residual extraction + inversion	Large-scale gravity anomalies	Initial GRACE-based framework	Noise; leakage	Han et al. [44]
	Direct differencing	~−7 mGal gravity decrease; consistent with theory	First spatial mapping of signal	Limited spatial resolution	Matsuo et al. [45]
	Time-series analysis	Co- & post-seismic signals	Introduced temporal evolution analysis	Temporal smoothing effect	Akhoondzadeh et al. [46]
	Topography-aware modeling	Topography is first-order effect	Improved interpretation	Model complexity	Li et al. [47]
	GPS + GRACE joint inversion	Layered Earth model improves fit	Multi-source constraint	Model assumptions	Zhou et al. [48]
	Northward GGC	Enhanced signal clarity	Improved detectability	Noise amplification	Li et al. [49]
Maule Chile earthquake	Gradient + decorrelation	Reduced striping noise	Improved signal extraction	Parameter sensitivity	Qu et al. [50]
Okhotsk earthquake	Hydrological correction + GNSS validation	Detectable deep-focus gravity signal	First detection of deep-focus event	Weak surface signal	Tanaka et al. [51]
Fiji earthquake	GRACE + GRACE-FO combined analysis	Consistent gravity change patterns	Multi-mission consistency	Model mismatch issues	Tanaka [52]

Notes: Coseismic gravity change refers to gravity perturbations induced by earthquake-related mass redistribution. Mass redistribution includes contributions from fault slip and associated crustal deformation. Density interface effects refer to gravity signals generated by vertical displacement of density boundaries such as the crust–mantle interface. Method categories (e.g., differencing, filtering, and gradient-based approaches) represent generalized data processing strategies for enhancing weak gravity signals.

summarizes the key methodological advances, highlighting the progressive enhancement of signal detectability and physical interpretability across diverse tectonic settings through iterative methodological improvements.

Overall, the methodological evolution summarized in Table 2 reflects a clear progression from simple signal detection to more sophisticated multi-stage processing frameworks, with early studies relying primarily on direct differencing or residual-based approaches that enabled the first identification of large-scale coseismic gravity signals yet suffered strong limitations from noise contamination and spatial leakage effects.

Subsequent developments introduced filtering-based techniques—including wavelet decomposition and spatial filtering—that significantly improve weak signal extraction through enhanced spatial coherence and high-frequency noise suppression, though these approaches tend to introduce signal attenuation and necessitate careful parameter tuning.

Recent studies have advanced toward gradient-based and multi-dataset integration methods, integrating GRACE/GRACE-FO observations with GNSS data or geophysical modeling constraints to improve spatial localization and physical consistency. These advances have also refined the physical interpretation of coseismic gravity signals—now recognized to stem from both fault slip-induced mass redistribution and density interface perturbations linked to vertical surface displacement, as demonstrated by studies of major earthquakes including the 2004 Sumatra–Andaman (Mw 9.1), 2010 Maule (Mw 8.8), and 2011 Tohoku (Mw 9.0). These integration frameworks enable more accurate discrimination between mass redistribution and surface deformation effects. Detection capability remains strongly tied to earthquake magnitude, focal mechanism, and depth. Shallow megathrust earthquakes ≥ Mw 8.0 are consistently detectable in spherical harmonic (SH) solutions, while smaller events (Mw < 7.5) and deep-focus earthquakes are far more difficult to resolve due to weaker surface deformation signals. Despite these advances, challenges remain in resolving weak or deep-seated signals—particularly for deep-focus earthquakes, where gravity perturbations approach the detection limit of current satellite gravimetry systems—underscoring the need for improved signal enhancement strategies and next-generation gravity missions with higher spatial and temporal resolution.

4.2.2. Monitoring of Postseismic Deep Mass Redistribution

Compared with coseismic observations, spherical harmonic (SH)-based GRACE products exhibit clear advantages in monitoring long-term postseismic gravity changes over timescales of several to tens of years. As a result, they have been widely employed to constrain mantle viscosity, evaluate viscoelastic rheological models, and infer deep mass redistribution following large earthquakes. Previous studies have demonstrated that GRACE time series are capable of capturing gravity recovery or persistent gravity evolution associated with some megathrust earthquakes over multi-year periods, providing critical observational constraints for regional mantle viscosity and for understanding slab sinking and deep mass transport processes.

Viscoelastic relaxation models constitute the primary theoretical framework for interpreting postseismic gravity and deformation signals. Among them, the Maxwell viscoelastic model, owing to its mathematical simplicity and clear physical interpretation, has long been used to describe long-term mantle flow and postseismic deformation [24,53]. However, this model shows limitations in reproducing the rapid decay commonly observed during the early postseismic stage. To address this issue, the Burgers rheological model, which incorporates transient viscoelastic behavior in addition to long-term viscous flow, has been introduced. This model has proven more effective in explaining postseismic deformation and gravity changes revealed by multi-source geodetic observations, including GPS, InSAR, and GRACE data [54,55].

Following the 2004 Sumatra–Andaman earthquake, numerous studies have quantified both coseismic and postseismic mass migration via equivalent water height anomalies, verifying that satellite gravimetry can directly resolve deep mass redistribution induced by great earthquakes and thereby offer a novel observational constraint on fault slip and mantle dynamics [56]. Subsequent investigations detected a prominent gravity reduction in the Andaman Sea, accompanied by a gradual postseismic relaxation process. Fitting the postseismic gravity time series with characteristic relaxation timescales revealed that the viscoelastic response of the mantle dominates the observed gravity variations, while also enabling quantification of the relative contributions from subsurface density redistribution and vertical surface deformation [41]. Furthermore, postseismic crustal dilatation derived from GRACE observations uncovered a close relationship between gravity changes and mantle upwelling, emphasizing the significance of deep material transport in postseismic deformation processes beyond shallow fault-slip behavior [40]. Collectively, these findings consistently indicate that postseismic gravity signals associated with the Sumatra–Andaman earthquake are mainly controlled by viscoelastic mantle relaxation and deep mass redistribution, yielding critical constraints on the rheological structure of the Earth’s interior. Analogous postseismic gravity evolution characteristics, yet with enhanced spatial resolution and clearer signal identification, were subsequently observed during the postseismic phase of the 2011 Tohoku earthquake.

For the 2011 Tohoku earthquake, long-term GRACE time series, following hydrological signal correction, reveal distinct coseismic and postseismic gravity anomalies, indicative of substantial disturbances to the regional gravity field [57]. Combined analyses of GPS and GRACE observations further demonstrate that postseismic deformation follows an exponential decay pattern consistent with Omori-type temporal attenuation, with cumulative displacements at far-field stations exceeding coseismic offsets, indicative of sustained long-term deformation. Meanwhile, GRACE measurements capture prominent gravity increases on both sides of the main rupture zone, with stronger signals observed on the oceanic side, reflecting asymmetric mass redistribution during the postseismic period [58]. These observations can be attributed to the combined effects of postseismic afterslip and viscoelastic relaxation, and integrated modeling frameworks incorporating multi-source geodetic data have been validated as effective in quantifying such dynamic processes. Additionally, gravity reductions detected in the back-arc region agree well with elastic dislocation models constrained by GPS observations, further verifying the sensitivity of satellite gravimetry to postseismic mass redistribution [59]. Overall, the 2011 Tohoku earthquake serves as a well-constrained case illustrating that the integration of GRACE and ground-based geodetic measurements can robustly constrain the spatiotemporal evolution of postseismic deformation and its underlying geodynamic mechanisms. Comparable postseismic gravity signals have also been reported for other large megathrust earthquakes, such as the 2010 Maule earthquake, further confirming the general applicability of viscoelastic relaxation models in explaining postseismic mass redistribution. For the 2010 Maule earthquake, GRACE observations reveal a broad regional gravity decrease to the east of the epicenter, spanning a spatial scale of approximately 500 km. This gravity reduction is primarily driven by crustal extension and surface subsidence, whereas weak offshore signals reflect the compensating effects of surface uplift and internal deformation. By integrating gravity observations with coseismic finite-fault slip models, these results illustrate that large-scale gravity measurements provide complementary constraints to surface geodetic and seismic datasets, yielding further insights into earthquake-induced mass redistribution and fault slip behavior [60]. Beyond megathrust earthquakes in subduction zones, GRACE observations have also been applied to large intraplate strike-slip events, exemplified by the 2012 Indian Ocean earthquake sequence (Mw 8.6 and Mw 8.2). Analyses combining long-term GRACE gravity data with GPS measurements, normal mode decomposition, and viscoelastic relaxation modeling indicate that postseismic viscoelastic relaxation dominates the observed gravity and deformation signals. These findings further confirm that GRACE can detect strike-slip earthquakes as small as approximately Mw 8.2, while providing key constraints on the rheological properties of the oceanic lithosphere and postseismic stress redistribution within intraplate oceanic domains [61].

Collectively, these case studies demonstrate that GRACE-derived spherical harmonic products can effectively resolve postseismic gravity signals across diverse tectonic settings, including both subduction-zone megathrust and intraplate strike-slip earthquakes. The observed gravity variations are consistently controlled by viscoelastic mantle relaxation and deep mass redistribution, underscoring the reliability of satellite gravimetry in constraining large-scale postseismic geodynamic processes.

4.2.3. Hydrological Noise and Advances in Signal Separation Techniques

Spherical harmonic (SH) products are highly sensitive to variations in terrestrial water storage (TWS), which often obscure earthquake-related solid Earth gravity signals under pronounced seasonal and interannual hydrological fluctuations [62]. Consequently, after spatial filtering, GRACE/GRACE-FO data analyses generally require additional leakage correction and signal separation to enhance the detectability of tectonic signals.

Spatial filtering methods, such as Gaussian and decorrelation filters (e.g., DDK), are commonly applied to suppress high-frequency noise, although they inevitably introduce spatial leakage and signal attenuation. To address these limitations, leakage correction techniques are employed, often based on hydrological or cryospheric models (e.g., GLDAS, WGHM, and CLM), using scale-factor approaches to reduce non-tectonic mass contributions.

Beyond hydrological correction, signal separation techniques are employed to extract specific geophysical components from mixed gravity observations. Widely used approaches include Signal separation methods commonly include empirical orthogonal function (EOF) [63] analysis (also referred to as principal component analysis, PCA) and independent component analysis (ICA). In addition, joint analyses integrating GRACE with GNSS and InSAR observations have been increasingly adopted to improve the robustness of signal separation and the physical consistency of inferred solid Earth processes [64,65].

To provide a systematic comparison of commonly used filtering and signal separation methods, their principles and applications in GRACE studies are summarized in

Table 3. Summary of filtering and signal separation methods for mitigating hydrological noise in GRACE data processing.

Method	Principle and Key Features	Applications in GRACE	Study
Gaussian Filter	Applies isotropic Gaussian kernel smoothing to suppress high-frequency noise; simple and robust but introduces spatial blurring	Widely used as a baseline filtering approach for GRACE SH solutions; removes short-wavelength noise prior to mass change inversion; commonly applied in global hydrological studies, large-scale mass variation analysis, and preprocessing before further signal extraction	[66]
DDK Filter	Uses error covariance matrix of SH coefficients for decorrelation and anisotropic filtering; reduces striping noise while preserving more signal	One of the most widely used filters in GRACE/GRACE-FO processing; effectively removes north–south striping noise; applied in hydrological mass change estimation, glacier and ice sheet mass balance studies, groundwater depletion analysis, and coseismic/postseismic gravity signal detection	[20,67]
PCA/EOF	Performs orthogonal transformation to extract dominant variance modes; widely used for dimensionality reduction and pattern recognition	Used to extract dominant spatiotemporal patterns in GRACE data; separates large-scale signals such as seasonal hydrological cycles and long-term trends; applied in climate variability studies and global mass redistribution analysis	[68,69]
ICA	Separates mixed signals based on statistical independence and non-Gaussianity; capable of isolating different geophysical sources	Applied to separate independent geophysical signals in GRACE data, such as hydrological, tectonic, and atmospheric components; useful in isolating earthquake-related gravity changes and regional hydrological anomalies	[70,71]
Slepian Functions	Constructs band-limited basis functions with optimal spatial energy concentration in a target region; minimizes leakage and enhances regional signal recovery	Widely used for regional mass change estimation; significantly reduces signal leakage in basin-scale hydrology, ice sheet mass balance, and earthquake-related gravity studies; particularly effective in small or coastal regions where traditional SH-based methods suffer from leakage	[72,73]

Notes: DDK filter refers to a decorrelation filtering approach based on the error covariance of spherical harmonic (SH) coefficients, designed to suppress north–south striping noise in GRACE data. Slepian functions are spatially localized basis functions that optimize signal concentration within a target region, thereby reducing signal leakage. Striping noise denotes correlated errors in GRACE SH solutions, typically appearing as north–south oriented artifacts. Signal leakage refers to the contamination of signals across adjacent regions due to spatial smoothing and limited resolution.

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The development of GRACE data processing methods reflects a transition from simple spatial filtering to more advanced statistical and physically constrained signal separation approaches. Early studies primarily relied on Gaussian filtering to suppress high-frequency noise in SH solutions; however, its isotropic smoothing inevitably resulted in signal leakage and spatial blurring. To overcome these limitations, improved filtering techniques such as the DDK filter were developed, incorporating prior error covariance information to reduce correlated striping noise and better preserve geophysical signals.

Beyond filtering, statistical decomposition methods including PCA and ICA were introduced to extract dominant spatiotemporal patterns and separate mixed geophysical signals. While these approaches are effective for identifying large-scale variability, their reliance on statistical assumptions and lack of spatial constraints limit their performance in regional applications. More recently, Slepian function-based approaches have been developed by introducing spatial localization into band-limited representations, significantly reducing leakage and improving the accuracy of regional mass change estimation.

Different hydrological noise reduction and signal separation methods show distinct advantages and applicability. As an isotropic smoothing technique, the Gaussian filter effectively suppresses high-frequency noise and improves the signal-to-noise ratio, yet may cause signal leakage and amplitude attenuation. The DDK filter, with an anisotropic design based on covariance information, performs well in mitigating striping noise in GRACE/GRACE-FO data while better retaining spatial signal features. For statistical methods, PCA/EOF helps extract dominant large-scale patterns, but suffers from limited physical interpretability and relies on orthogonality rather than independence. By comparison, ICA is more capable of separating mixed, non-Gaussian and statistically independent signals, making it suitable for multi-signal scenarios, despite its sensitivity to preprocessing and parameter selection. Slepian functions, featuring strong spatial localization and spectral concentration, excel in regional-scale analyses by reducing leakage and enhancing signal recovery within targeted regions. In general, these methods are complementary: filtering approaches (Gaussian, DDK) target noise suppression, statistical methods (PCA/EOF, ICA) focus on signal decomposition, and Slepian functions emphasize regional localization. Combinations of these strategies have been increasingly applied in practical studies. In practice, the choice of an appropriate filtering or signal separation method should be guided by the spatial scale of the study region and the signal-to-noise characteristics [74].

4.3. Comparison Between Mascon and SH Products

In earthquake-related gravity studies, GRACE Mascon products and spherical harmonic (SH) solutions differ fundamentally in their representation of gravity signals and data processing strategies, which directly affects their ability to resolve the spatial structure of coseismic gravity changes. Mascon products estimate gravity anomalies by spatially averaging mass variations within predefined regions, a strategy that improves time-series stability and suppresses random noise but tends to introduce smoothing near fault boundaries and areas with strong deformation gradients, leading to an attenuation of high-spatial-gradient signals such as coseismic gravity gradients and limiting the representation of fine-scale structures compared with SH products.

For large earthquakes, both Mascon and SH products can robustly detect prominent coseismic and postseismic gravity changes, and their spatial patterns are generally consistent with predictions from elastic or viscoelastic models, indicating that the two products contain comparable physical information when signals are strong and spatially extensive. In studies of moderate-magnitude earthquakes or analyses focused on localized tectonic features, the sensitivity of Mascon products to small-scale mass redistribution may be reduced due to the influence of prior constraints and spatial averaging.

Differences in noise treatment and effective spatial resolution further shape the performance of the two products in seismic applications. Mascon products effectively suppress the characteristic north–south striping noise during the inversion process and can usually be applied directly without extensive post-processing, whereas most official Mascon solutions rely on uniform background corrections and fixed filtering parameters that do not fully capture time-varying noise characteristics or event-specific differences. SH products are more sensitive to striping noise but offer greater flexibility during post-processing, allowing users to select decorrelation and smoothing strategies tailored to individual earthquakes, such as P3M6 filtering or Gaussian smoothing with different radii, thereby balancing noise reduction and the preservation of spatial details in coseismic gravity fields.

Overall, Mascon products are well suited for stable monitoring of gravity changes associated with large earthquakes at regional to global scales and for long-term postseismic analysis, while SH products retain clear advantages in resolving detailed coseismic gravity structures and in quantitative comparisons with geophysical models. Given their complementary characteristics in spatial resolution, noise behavior, and processing flexibility, an increasing number of studies advocate the combined use of Mascon and SH products to improve the robustness of earthquake gravity analyses and to advance the understanding of the physical mechanisms underlying earthquake-related mass redistribution.

5. Discussion

Satellite gravimetry still faces several limitations in earthquake monitoring, including relatively low spatial resolution, a high magnitude detection threshold, and significant interference from non-tectonic signals, which constrain its capability to resolve and interpret earthquake-related gravity changes [12].

5.1. Limited Spatial Resolution

The Level-2 spherical harmonic (SH) products from GRACE and GRACE-FO are conventionally expanded to degree and order 60, yielding an effective half-wavelength resolution of 300–400 km that restricts the recovery of localized coseismic gravity signals near epicenters; post-processing filters applied to suppress north–south stripe noise further introduce spatial smoothing and signal attenuation [75,76].

Mascon solutions alleviate these issues by parameterizing mass variations over discrete spatial blocks and imposing spatial regularization within inversions. While mascon products are often provided on grids as fine as 0.5° × 0.5°, their effective resolution is comparable to a Gaussian smoothing radius of 210–270 km, varying with processing center and regularization scheme [35,77].

Relative to SH solutions, mascon approaches reduce signal leakage and striping artifacts via spatial localization and Tikhonov-type regularization, improving the recovery of regional mass anomalies and the preservation of tectonic deformation gradients. Both solution types remain fundamentally constrained, however, by satellite observational geometry and the ill-posed character of gravity field inversion.

Traditional GRACE Level-2 SH solutions from CSR, GFZ and JPL (RL06) are commonly truncated at degree and order 60–96, giving an effective spatial resolution of ~300–400 km after standard filtering, which severely limits the characterization of localized mass redistribution during earthquakes. To improve spatial resolution, advanced spectral-domain regularization strategies have been developed. Chen et al. integrated spatial constraints from filtered GRACE mass change fields into the SH coefficient inversion, suppressing high-degree noise amplification while enhancing the stability and fidelity of recovered gravity signals. The Tongji-RegGrace2019 solution extends the SH expansion to degree and order 180, achieving an effective spatial scale of approximately 1° (~110 km). This represents a marked resolution improvement over conventional RL06 products, shifting from the ~300 km scale of filtered SH solutions to a much finer representation while preserving physically consistent signal structures for small-scale geophysical studies [78].

5.2. High Magnitude Detection Threshold

Gravity changes associated with small-magnitude earthquakes are generally weak and readily obscured by noise in GRACE observations, yielding low signal-to-noise ratios (SNR) that hinder the reliable extraction of seismic signals. Seismically induced gravity variations can also be masked by concurrent geophysical signals including hydrological mass changes, oceanic variability and atmospheric loading, further complicating the isolation of tectonic signals [19].

GRACE observations are thus predominantly sensitive to large earthquakes, with existing studies indicating a practical detection threshold of approximately Mw 7.5–8.0. This threshold is governed by the combined effects of measurement noise, spatial smoothing and signal leakage, all of which reduce the observability of small-scale coseismic mass redistribution [36].

Effective spatial resolution of gravity field solutions plays a critical role in earthquake detectability. Higher spatial resolution suppresses signal leakage and spatial averaging, strengthens the contrast between coseismic signals and background noise, and improves effective SNR. This not only increases the potential for detecting moderate-magnitude events under favorable conditions, but also refines the characterization of spatial gradients in mass redistribution closely linked to fault slip heterogeneity and rupture complexity, thereby enhancing both the detectability and physical interpretability of GRACE-derived earthquake signals. Beyond detectability, improved spatial resolution has direct implications for earthquake physics. It enhances the ability to resolve spatial gradients of coseismic mass redistribution, which are closely linked to fault slip heterogeneity and rupture complexity [74].

In this context, Fatolazadeh et al. introduced the concept of gravity field deformation and proposed an epicenter localization approach based on invariants of the gravity strain tensor, which is independent of reference coordinates and directly reflects tectonically driven mass redistribution [79]. By enhancing signal coherence through localized wavelet analysis, their method successfully identified epicenters of shallow earthquakes down to Mw ~7.5 using GRACE-derived gravity strain invariants, demonstrating that advanced signal processing techniques can partially overcome traditional detection limits and extend the applicable magnitude range of GRACE-based earthquake analysis.

5.3. Limited Capability in Resolving Earthquake Source Mechanisms

Earthquakes induce crustal mass redistribution that generates detectable gravity field perturbations observable by GRACE and GRACE-FO. As these gravity data reflect spatially integrated mass changes, they offer limited ability to directly resolve detailed source parameters such as fault geometry and rupture kinematics. In contrast, InSAR delivers high-resolution surface deformation measurements at meter to sub-kilometer scales, enabling detailed mapping of fault slip and near-field deformation. GNSS/GPS observations provide an important complementary geodetic constraint by offering continuous, high-precision three-dimensional ground displacement measurements. Compared with InSAR, which provides high-resolution spatial coverage but is limited by temporal sampling and line-of-sight geometry, GNSS offers superior temporal resolution and absolute positioning information, making it particularly useful for capturing transient deformation processes and validating InSAR-derived deformation fields. Therefore, GNSS is often jointly used with InSAR to improve the robustness of geodetic constraints on earthquake source modeling.

GRACE, InSAR, and GNSS are complementary geodetic techniques that capture different aspects of the earthquake deformation process: GRACE senses large-scale mass redistribution, InSAR captures high-resolution surface deformation, and GNSS provides continuous three-dimensional displacement constraints. This complementarity offers clear advantages for earthquake studies. GRACE resolves large-scale, deep-seated mass changes poorly captured by surface data, especially in offshore or low-coherence InSAR regions, while InSAR provides fine near-field deformation constraints beyond GRACE’s resolution. Joint analysis of these datasets thus improves the robustness of source modeling and reduces fault slip uncertainties [80,81,82].

Owing to differences in spatial and temporal resolution, data characteristics, and measurement geometries among GRACE, InSAR, and GNSS observations, their effective integration requires more sophisticated preprocessing and data fusion strategies, which remain an important topic for future research. Finally, GRACE/GRACE-FO observations can be integrated with forward geophysical models to indirectly constrain earthquake source parameters, despite the difficulty of direct inversion. By comparing observed gravity changes with model predictions, satellite gravimetry provides independent constraints on large-scale and deep-seated mass redistribution, complementing surface-based observations and improving the interpretation of earthquake processes.

6. Conclusions

This study reviews the workflow and key advantages of GRACE and GRACE-FO satellite gravimetry for earthquake monitoring. Owing to their global coverage, these missions enable the detection of mass changes occurring at both the Earth’s surface and in the deep interior, including over oceanic regions where ground-based observations are limited. This capability makes satellite gravimetry particularly suitable for investigating earthquake-induced mass redistribution at the global scale.

Unlike surface displacement-based techniques such as InSAR and GNSS, GRACE and GRACE-FO characterize earthquake-related processes through variations in the Earth’s gravity field. This approach provides complementary information on coseismic mass changes and offers an alternative perspective for examining the influence of earthquakes on subsurface mass redistribution and internal Earth structure.